One mouse study found that vaccine injection without aspiration did significantly increase the risk of adverse cardiac events. That research hasn't been reproduced in humans but this area deserves further investigation. At least early in the pandemic, US healthcare providers weren't routinely aspirating.
I don't know the injection practices in Germany. The WHO and US CDC no longer recommend aspiration prior to intramuscular injection, mainly over pain management concerns. (I'm not claiming this is a good idea, just pointing out the current injection protocol.)
In practice there is a wide variance between US healthcare providers depending on where they work and how they were trained. Some aspirate, some don't, some try but use the wrong technique.
... What? Here in Germany, that's like one of the basic things that people who deal with needles on anything alive learn.